Solution

The solution to the riddle is actually quite simple and it turns out that you only need to use the scale once. I actually did not realize this when I asked the problem. The basic idea is to weight powers of 2 from each box of balls.

If you put 1 ball from box 1, 2 balls from box 2, 4 balls from box 3, 8 balls from box 4 and 16 balls from box 5 you can map the resulting number to exactly which box has the heavy balls and which has the light balls.

To do this simply take the weight the scale displays, subtract 31 (the total number of balls) and consider that number. If you multiply it by 10, its value, which I will call N, is the number of heavy balls minus the number of light balls.

If we consider the absolute value of N, its possible values and the resulting conclusions are:

1 --> boxes 1 and 2 have the heavy and light balls
2 --> boxes 2 and 3 have the heavy and light balls
3 --> boxes 1 and 3 have the heavy and light balls
4 --> boxes 3 and 4 have the heavy and light balls
6 --> boxes 2 and 4 have the heavy and light balls
7 --> boxes 1 and 4 have the heavy and light balls
8 --> boxes 4 and 5 have the heavy and light balls
12 -> boxes 3 and 5 have the heavy and light balls
14 -> boxes 2 and 5 have the heavy and light balls
15 -> boxes 1 and 5 have the heavy and light balls

If N is negative then the lower number box has the heavy balls and the higher numbered box from the chart above has the light balls. Otherwise, vice-versa

Prize

This weeks one SBD prize went to @uber-dragon. He is our first repeat winner! Congratulations and thanks to everyone who participated!

Don't forget to follow and to check out my past riddles

First off, thanks to everyone for all the support! If you'd like to browse my older riddles you can do so at the links below:

https://steemit.com/life/@droopy/steem-riddle-of-the-week-2-flipping-cards-prize-doubled
https://steemit.com/life/@droopy/steem-riddle-of-the-week-3-alternating-truth-prize-for-first-correct-answer
https://steemit.com/life/@droopy/steem-riddle-of-the-week-4-black-cards-prize-for-first-correct-answer
https://steemit.com/life/@droopy/steem-riddle-of-the-week-5-the-cup-game-prize-for-first-correct-answer
https://steemit.com/life/@droopy/steem-riddle-of-the-week-6-burning-ropes-prize-doubled
https://steemit.com/life/@droopy/steem-riddle-of-the-week-7-midpoints
https://steemit.com/life/@droopy/steem-riddle-of-the-week-8-truth-lies-and-chaos
Prize

This weeks one SBD prize went to @uber-dragon. Congratulations and thanks to everyone who participated!

Don't forget to follow and to check out my past riddles

First off, thanks to everyone for all the support! If you'd like to browse my older riddles you can do so at the links below:

Steem Riddle of the Week #10: Weighted Balls -- Solution Revealed + Prize awared

Solution

Prize